Defining parameters
Level: | \( N \) | = | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 20 \) | ||
Newform subspaces: | \( 83 \) | ||
Sturm bound: | \(42336\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(441))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14592 | 10938 | 3654 |
Cusp forms | 13632 | 10502 | 3130 |
Eisenstein series | 960 | 436 | 524 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(441))\)
We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(441))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(441)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)